(1.2) In (1.1), given a particular futures price path from Jul to Sep, you computed the total deposit required to keep your futures positions alive. Let's call this amount TD. You are at the beginning of October right now and want to start a new trade of long 2 futures contracts for the upcoming 90 trading days. In this question, you will simulate 1,000 futures price paths and get a distribution of TD for your new trade. This computation helps you more precisely estimate the amount of money required for your futures position. In particular, this exercise allows you to answer questions like "What's the probability that your futures position will stay alive for up to 90 trading days?". To do this, you first need a model for the futures price dynamics. (30) a) Suppose the daily log return on the futures price is modeled as a linear trend plus a normal random noise. That is, assuming the daily log return is ln(Ft+1)ln(Ft)=+, where is a standard normal random variable (N(0,1) distributed) and at different dates are independent. Use the data in (1.1) to estimate the drift and the standard deviation of the noise term (no need to annualize the numbers for these). Report your results. (Hint: compute log returns for (1.1) and estimate the sample mean and the standard deviation.) b) Given your estimated parameters, simulate the daily returns for 90 trading days, map each return path back to a futures price path, and compute the TD corresponding to this simulated futures price path as you did in (1.1). When doing the simulation, use the latest available futures price in (1.1) as F0. Repeat this step 1,000 times and record the resulting 1,000 values of TD with "Excel What-if Analysis - Data Table". (Hint: a brief tutorial for Data Table that may be helpful is included in the Midterm Project folder. For other tutorials for Data Table, there are many online resources.) 2 c) Now you have a distribution of the TD. You may compute a VaR type of measure of TD, i.e., what is the minimum amount of money you need to keep your futures position (long 2 contracts) alive for 90 trading days with a 95% chance